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India and China have many similarities. Both is some kind of "multicultural" (in classic terms) Empires with rich history of state building and with existing culture (compared to Africa for example). They both experienced European pressure, India was simply conquered and made into official part of British Empire, China was forced to became colony-like dependent state by Europeans and neighbors in 19th century.
But for some reason India didn't progress much as China. Maybe root is in culture and historical background. I don't know about India much, but people said that it is more "anarchistic" inside, i.e. people have more laid-back attitude overall. Chinese, on other side, have rich legalist history.
Of course is it hard to compare countries, because even some small happenings in history may end in different outcomes.
But there are other large populated countries like Indonesia or Nigeria, and they still don't show Chinese-style economic growth. Although in terms of outsourcing they better on paper for cheap labor.